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Nonlinear least squares — the Levenberg algorithm revisited*

Published online by Cambridge University Press:  17 February 2009

M. R. Osborne
M. R. Osborne
Affiliation:
Computer Centre, Australian National University, Canberra, A. C. T. 2601, Australia.
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Abstract

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One of the most succesful algorithims for nonlinear least squares calculations is that associated with the names of Levenberg, Marquardt, and Morrison. This algorithim gives a method which depends nonlinearly on a parameter γ for computing the correction to the current point. In this paper an attempt is made to give a rule for choosing γ which (a) permits a satisfactory convergence theorem to be proved, and (b) is capable of satisfactory computer implementation. It is beleieved that the stated aims have been met with reasonable success. The convergence theorem is both simple and global in character, and a computer code is given which appears to be at least competitive with existing alternatives.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 3 , June 1976 , pp. 343 - 357
Copyright
Copyright © Australian Mathematical Society 1976

References

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